THE LOGIC OF CAUSAL PROPOSITIONS

 1. PROPOSITIONAL LOGIC

Propositions are statements which that are a fundamental element in reasoning. Their peculiarity character is that they assert that something is the case or that something is not the case. Their statement can be true or false. Propositions are therefore statements that have a truth-value, that is, they have the property of being true / false.

Different from propositions, questions, commands and exams. Only propositions can be confirmed or rejected. Questions can be asked, given commands and surprises can be expressed but none of them can be confirmed or denied or judged to be true or false. What is different from other branches of projection logic is that theoretical logic does not deal with logical relationships and properties that involve smaller parts than simple expressions with a statement

2. The Language of Propositional Logic 

Propositional logic may be studied through a formal method in which formulas of a formal language may be interpreted to represent propositions. A system of axioms and inference rules allows certain formula to be derived. These derivatives are called theorems and can be interpreted to be true propositions. Logical relationships can be found in natural languages. In English for example, some examples are "and" (conjunction), "or" (disjunction) and "not" (negation) 

2.1 Syntax and Formation Rules of PL

In any ordinary language, a statement will never consist of a single word, but would always at the very least consist of a noun or pronoun with a verb. However, the PL language uses capital letters ‘A’, ‘B’, ‘C’ instead of whole expressions, as theoretical logic ignores small parts of expressions and treats simple expressions as inseparable whole. Real active operators use logical codes.  

2.2. Truth Functions and Truth Tables

True-functional propositional logic does not analyze parts of simple statements, but considers the methods of consolidation that the whole truth or falsehood depends entirely on the truth or falsity of the parts. A truth table is a table representation of all the values for the inputs and the corresponding outputs. It is a mathematical table that shows all possible outcomes from all instances where it is considered to be true.

Consider the example:

• (P1). Good actions give strength to ourselves.
• (P2). It doesn't inspire good actions in others.
• (P3). Good actions give strength to ourselves and inspire good actions in others.

P1	P2	NOT P2	P1AND (NOT P2)
T	T	F	F
T	F	T	T
F	T	F	F
F	F	T	F

                   (P3) = (P1) AND (NOT P2)     

REFERENCES:

Propositions and Arguments / Matthew Knachel Senior Lecturer (Philosophy) at University of Wisconsin - Milwaukee:https://human.libretexts.org/Bookshelves/Philosophy/Book%3A_Fundamental_Methods_of_Logic_(Knachel)/1%3A_The_Basics_of_Logical_Analysis/1.2%3A_Basic_Notions_-_Propositions_and_Arguments#title ( Click here )